Modus tollens is a rule of logical inference. We use rules of inference when we argue from a set of premises to a conclusion, for example when we prove that the Pythagorean Theorem follows from Euclid's Axioms. Roughly, modus tollens means "way of removing," alluding to the fact that one of the relevant premises is negated or "removed."

Faced with propositions of certain forms, a rule of inference tells you how to logically combine them to derive valid conclusions. In particular, modus tollens tells you what propositions you can derive from a conditional proposition and the negation of its consequent. A conditional is a proposition of the form "if A then B." A conditional is made up of two parts, the antecedent, the part preceded by if, i.e., "A", and the consequent, the part followed by "then," i.e., "B." The negation of the consequent...